Design and implement an Object-Oriented program that sorts two unsorted arrays of English alphabet letters in alphabetical order (i.e., from A-Z); the first array contains 11 English letters, and the second array contains 15 English letters. Then, the program must merge the two sorted arrays in another array (produce a third sorted array). In addition, the program must apply the sequential search algorithm to find and show how many occurrences of a specific English alphabet letter is available in the third sorted array.